The next step is to deal with the more stubborn dirt. You don’t necessarily need special cleaning agents for this because a good result can be achieved through cheaper methods. Just put a few drops of dishwasher detergent in about one liter of water, dip your microfiber cloth into the water, and wring it out properly so that it is only slightly moist. You only want to wipe your screen and not wash it. Make sure no water runs down the screen and into the interior, otherwise it will damage the electronics. Now repeat the dry cleaning procedure with the damp cloth.
At the end of the cleaning process, carefully wipe your laptop screen dry with a lint-free cloth. This is important to prevent streaks from appearing. Using a damp cloth you might use to clean eyeglasses may not be a good idea as it can leave behind a film that can attract dust.